Some silly question on oscillators

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    Oscillators
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Discussion Overview

The discussion revolves around the harmonic oscillator and damped oscillator equations, specifically focusing on the phase difference (d) in the solutions. Participants explore scenarios where the phase difference is zero versus when it takes on other values, particularly in the context of initial conditions and types of motion.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant notes that the typical solution for the harmonic oscillator is x=Acos(wt+d) and questions why the phase difference d is often considered zero in many intermediate mechanics problems.
  • Another participant raises a similar question regarding damped oscillators, indicating a broader interest in the topic.
  • A participant suggests that if there is motion at t=0, such as starting the oscillator with an impulse, this could affect the phase difference.
  • It is proposed that if the representation x=Asin(wt+d) is used and the spring is released at t=0, then d would equal pi/2 radians (90 degrees), indicating a different initial condition.

Areas of Agreement / Disagreement

Participants express differing views on the value of the phase difference d, with some suggesting it is zero in certain cases while others propose it can take on specific values depending on initial conditions. The discussion remains unresolved regarding the general applicability of these conditions.

Contextual Notes

Participants do not fully explore the implications of different initial conditions on the phase difference, and there may be assumptions regarding the definitions of motion and release conditions that are not explicitly stated.

marmot
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Ok

i know that the solution for the harmonic oscillator differential equation is

x=Acos(wt+d)

However,

I also know that most of the time, atleast in average intermediate mechanics problems the phase difference, d is zero. this baffles me a lot. for example if there is a spring and i stretch it 10 cm and let it go, i know that the phase difference is zero because cosine starts from a maximum and the 10cm i stretched are going to be the maximum. but when does d actually is a value?
 
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same question for damped oscillators btw
 
If there is motion at t=0. For instance if you start it by an impulse.
 
If you use the representation x = Asin(wt + d), and you release the spring at t = 0, then d = pi/2 radians (90 degrees).
 

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